Question: Determine the value of the following complex number power. Your answer will be plotted in orange. $ ({ e^{\pi i / 3}}) ^ {3} $
Solution: Since $(a ^ b) ^ c = a ^ {b \cdot c}$ $ ({ e^{\pi i / 3}}) ^ {3} = e ^ {3 \cdot (\pi i / 3)} $ The angle of the result is $3 \cdot \frac{1}{3}\pi$ , which is $\pi$ Our result is $ e^{\pi i}$.